They were once among New York’s most powerful political figures: Sheldon Silver, the former Democratic speaker of the State Assembly, and Dean G. Skelos, the onetime Republican leader of the State Senate. Then, both men were convicted in federal corruption trials, only to have the verdicts overturned on appeal.

Now, with Senator Robert Menendez, Democrat of New Jersey, found guilty of corruption charges in the Southern District of New York, his lawyers say they will appeal his conviction aggressively and believe he, too, will be vindicated.

Defense lawyers make such claims routinely, but in the realm of federal corruption cases, they may have reason to be optimistic. The U.S. Supreme Court, in rulings since 2010, has narrowed the legal definition of corruption, resulting in a number of convictions of political figures in New York and elsewhere being overturned.

“We have seen the capacity of appeals courts to surprise us all,” said Martin S. Bell, a former Southern District corruption prosecutor. “If Yogi Berra were to be heard on this, he’d probably say, it ain’t really over until the appeals court sings.”

Still, Mr. Bell and other legal experts said, prosecutors are learning to work within the new rules in ways that may withstand scrutiny from potentially skeptical higher courts.

At Mr. Menendez’s trial, prosecutors presented evidence of a brazen plot in which, they said, the senator and his wife accepted bribes of gold bullion, hundreds of thousands of dollars in cash and a Mercedes-Benz in exchange for his agreeing to do political favors at home and abroad. As part of the scheme, prosecutors said, Mr. Menendez steered weapons and aid to Egypt.